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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 08:38:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444376449rsr9js1d9n980du.htm/, Retrieved Sat, 25 May 2024 05:12:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281710, Retrieved Sat, 25 May 2024 05:12:43 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 07:38:46] [935c69a10ec4a64678755fcf1ddf3064] [Current]
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Dataseries X:
0,62
0,7
1,65
1,79
2,28
2,46
2,57
2,32
2,91
3,01
2,87
3,11
3,22
3,38
3,52
3,41
3,35
3,68
3,75
3,6
3,56
3,57
3,85
3,48
3,65
3,66
3,36
3,19
2,81
2,25
2,32
2,85
2,75
2,78
2,26
2,23
1,46
1,19
1,11
1
1,18
1,59
1,51
1,01
0,9
0,63
0,81
0,97
1,14
0,97
0,89
0,62
0,36
0,27
0,34
0,02
-0,12
0,09
-0,11
-0,38




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281710&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281710&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281710&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.003666666666670.16319756261796412.2775526455449
Geometric MeanNaN
Harmonic Mean0.735113908832323
Quadratic Mean2.36348330506761
Winsorized Mean ( 1 / 20 )2.006333333333330.16186657801168512.3949820770814
Winsorized Mean ( 2 / 20 )2.004333333333330.16137410770174612.420414661798
Winsorized Mean ( 3 / 20 )2.009833333333330.1597907338528612.5779091495008
Winsorized Mean ( 4 / 20 )2.013833333333330.15870220338640112.6893848375258
Winsorized Mean ( 5 / 20 )2.024666666666670.15499798917351913.0625350526327
Winsorized Mean ( 6 / 20 )2.028666666666670.15315799358217213.2455813713585
Winsorized Mean ( 7 / 20 )2.029833333333330.15252479499580513.3082187285626
Winsorized Mean ( 8 / 20 )2.059166666666670.14548774225002414.1535405995094
Winsorized Mean ( 9 / 20 )2.053166666666670.14447498789776814.2112257390844
Winsorized Mean ( 10 / 20 )2.043166666666670.14226804725342714.3613882815662
Winsorized Mean ( 11 / 20 )2.05050.13923974873260414.726398306979
Winsorized Mean ( 12 / 20 )2.06850.13504504898083915.3171109611985
Winsorized Mean ( 13 / 20 )2.083666666666670.13199554149863515.785886727759
Winsorized Mean ( 14 / 20 )2.055666666666670.12680791262508616.2108706319009
Winsorized Mean ( 15 / 20 )2.065666666666670.12296969602044116.7981765712692
Winsorized Mean ( 16 / 20 )2.044333333333330.11970664865653917.0778595531391
Winsorized Mean ( 17 / 20 )2.02450.11420281913466517.7272331396019
Winsorized Mean ( 18 / 20 )1.99750.10942985912353518.2537016496114
Winsorized Mean ( 19 / 20 )2.01650.10285523395793919.6052249594281
Winsorized Mean ( 20 / 20 )2.019833333333330.10043000532643720.1118513014918
Trimmed Mean ( 1 / 20 )2.012931034482760.16052187436253712.5399173319929
Trimmed Mean ( 2 / 20 )2.020.15874610129173212.7247219526217
Trimmed Mean ( 3 / 20 )2.02870370370370.15674939746490612.9423381302496
Trimmed Mean ( 4 / 20 )2.035961538461540.15488726489839713.1447962477553
Trimmed Mean ( 5 / 20 )2.04260.15283385937490613.3648394953466
Trimmed Mean ( 6 / 20 )2.047083333333330.1513224676442613.5279536819725
Trimmed Mean ( 7 / 20 )2.051086956521740.14975801036244113.6960083240806
Trimmed Mean ( 8 / 20 )2.055227272727270.1477232029037713.9126909810241
Trimmed Mean ( 9 / 20 )2.054523809523810.14674565067087714.0005771900642
Trimmed Mean ( 10 / 20 )2.054750.1454264231537114.1291379890998
Trimmed Mean ( 11 / 20 )2.056578947368420.14392747319870514.2889950171578
Trimmed Mean ( 12 / 20 )2.05750.14235456237357314.4533477936634
Trimmed Mean ( 13 / 20 )2.055882352941180.14091888265200414.5891190325297
Trimmed Mean ( 14 / 20 )2.0518750.13928926554464914.731034670739
Trimmed Mean ( 15 / 20 )2.051333333333330.13794446103233714.8707191139227
Trimmed Mean ( 16 / 20 )2.049285714285710.13651455779438315.0114811738418
Trimmed Mean ( 17 / 20 )2.050.13473050023030315.2155599251529
Trimmed Mean ( 18 / 20 )2.053750.13306968385349715.4336430396955
Trimmed Mean ( 19 / 20 )2.062272727272730.13118166218156915.7207394156839
Trimmed Mean ( 20 / 20 )2.06950.12967667282007315.9589227190571
Median2.255
Midrange1.735
Midmean - Weighted Average at Xnp2.0141935483871
Midmean - Weighted Average at X(n+1)p2.05133333333333
Midmean - Empirical Distribution Function2.0141935483871
Midmean - Empirical Distribution Function - Averaging2.05133333333333
Midmean - Empirical Distribution Function - Interpolation2.05133333333333
Midmean - Closest Observation2.0141935483871
Midmean - True Basic - Statistics Graphics Toolkit2.05133333333333
Midmean - MS Excel (old versions)2.051875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.00366666666667 & 0.163197562617964 & 12.2775526455449 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.735113908832323 &  &  \tabularnewline
Quadratic Mean & 2.36348330506761 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.00633333333333 & 0.161866578011685 & 12.3949820770814 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.00433333333333 & 0.161374107701746 & 12.420414661798 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.00983333333333 & 0.15979073385286 & 12.5779091495008 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.01383333333333 & 0.158702203386401 & 12.6893848375258 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.02466666666667 & 0.154997989173519 & 13.0625350526327 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.02866666666667 & 0.153157993582172 & 13.2455813713585 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.02983333333333 & 0.152524794995805 & 13.3082187285626 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.05916666666667 & 0.145487742250024 & 14.1535405995094 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.05316666666667 & 0.144474987897768 & 14.2112257390844 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.04316666666667 & 0.142268047253427 & 14.3613882815662 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.0505 & 0.139239748732604 & 14.726398306979 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.0685 & 0.135045048980839 & 15.3171109611985 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.08366666666667 & 0.131995541498635 & 15.785886727759 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.05566666666667 & 0.126807912625086 & 16.2108706319009 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.06566666666667 & 0.122969696020441 & 16.7981765712692 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.04433333333333 & 0.119706648656539 & 17.0778595531391 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.0245 & 0.114202819134665 & 17.7272331396019 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.9975 & 0.109429859123535 & 18.2537016496114 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.0165 & 0.102855233957939 & 19.6052249594281 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.01983333333333 & 0.100430005326437 & 20.1118513014918 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.01293103448276 & 0.160521874362537 & 12.5399173319929 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.02 & 0.158746101291732 & 12.7247219526217 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.0287037037037 & 0.156749397464906 & 12.9423381302496 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.03596153846154 & 0.154887264898397 & 13.1447962477553 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.0426 & 0.152833859374906 & 13.3648394953466 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.04708333333333 & 0.15132246764426 & 13.5279536819725 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.05108695652174 & 0.149758010362441 & 13.6960083240806 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.05522727272727 & 0.14772320290377 & 13.9126909810241 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.05452380952381 & 0.146745650670877 & 14.0005771900642 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.05475 & 0.14542642315371 & 14.1291379890998 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.05657894736842 & 0.143927473198705 & 14.2889950171578 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.0575 & 0.142354562373573 & 14.4533477936634 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.05588235294118 & 0.140918882652004 & 14.5891190325297 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.051875 & 0.139289265544649 & 14.731034670739 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.05133333333333 & 0.137944461032337 & 14.8707191139227 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.04928571428571 & 0.136514557794383 & 15.0114811738418 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.05 & 0.134730500230303 & 15.2155599251529 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.05375 & 0.133069683853497 & 15.4336430396955 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.06227272727273 & 0.131181662181569 & 15.7207394156839 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.0695 & 0.129676672820073 & 15.9589227190571 \tabularnewline
Median & 2.255 &  &  \tabularnewline
Midrange & 1.735 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.0141935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.05133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.0141935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.05133333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.05133333333333 &  &  \tabularnewline
Midmean - Closest Observation & 2.0141935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.05133333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.051875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281710&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]2.00366666666667[/C][C]0.163197562617964[/C][C]12.2775526455449[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.735113908832323[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.36348330506761[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.00633333333333[/C][C]0.161866578011685[/C][C]12.3949820770814[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.00433333333333[/C][C]0.161374107701746[/C][C]12.420414661798[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.00983333333333[/C][C]0.15979073385286[/C][C]12.5779091495008[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.01383333333333[/C][C]0.158702203386401[/C][C]12.6893848375258[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.02466666666667[/C][C]0.154997989173519[/C][C]13.0625350526327[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.02866666666667[/C][C]0.153157993582172[/C][C]13.2455813713585[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.02983333333333[/C][C]0.152524794995805[/C][C]13.3082187285626[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.05916666666667[/C][C]0.145487742250024[/C][C]14.1535405995094[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.05316666666667[/C][C]0.144474987897768[/C][C]14.2112257390844[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.04316666666667[/C][C]0.142268047253427[/C][C]14.3613882815662[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.0505[/C][C]0.139239748732604[/C][C]14.726398306979[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.0685[/C][C]0.135045048980839[/C][C]15.3171109611985[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.08366666666667[/C][C]0.131995541498635[/C][C]15.785886727759[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.05566666666667[/C][C]0.126807912625086[/C][C]16.2108706319009[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.06566666666667[/C][C]0.122969696020441[/C][C]16.7981765712692[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.04433333333333[/C][C]0.119706648656539[/C][C]17.0778595531391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.0245[/C][C]0.114202819134665[/C][C]17.7272331396019[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.9975[/C][C]0.109429859123535[/C][C]18.2537016496114[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.0165[/C][C]0.102855233957939[/C][C]19.6052249594281[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.01983333333333[/C][C]0.100430005326437[/C][C]20.1118513014918[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.01293103448276[/C][C]0.160521874362537[/C][C]12.5399173319929[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.02[/C][C]0.158746101291732[/C][C]12.7247219526217[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.0287037037037[/C][C]0.156749397464906[/C][C]12.9423381302496[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.03596153846154[/C][C]0.154887264898397[/C][C]13.1447962477553[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.0426[/C][C]0.152833859374906[/C][C]13.3648394953466[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.04708333333333[/C][C]0.15132246764426[/C][C]13.5279536819725[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.05108695652174[/C][C]0.149758010362441[/C][C]13.6960083240806[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.05522727272727[/C][C]0.14772320290377[/C][C]13.9126909810241[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.05452380952381[/C][C]0.146745650670877[/C][C]14.0005771900642[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.05475[/C][C]0.14542642315371[/C][C]14.1291379890998[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.05657894736842[/C][C]0.143927473198705[/C][C]14.2889950171578[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.0575[/C][C]0.142354562373573[/C][C]14.4533477936634[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.05588235294118[/C][C]0.140918882652004[/C][C]14.5891190325297[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.051875[/C][C]0.139289265544649[/C][C]14.731034670739[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.05133333333333[/C][C]0.137944461032337[/C][C]14.8707191139227[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.04928571428571[/C][C]0.136514557794383[/C][C]15.0114811738418[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.05[/C][C]0.134730500230303[/C][C]15.2155599251529[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.05375[/C][C]0.133069683853497[/C][C]15.4336430396955[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.06227272727273[/C][C]0.131181662181569[/C][C]15.7207394156839[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.0695[/C][C]0.129676672820073[/C][C]15.9589227190571[/C][/ROW]
[ROW][C]Median[/C][C]2.255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.735[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.0141935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.05133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.0141935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.05133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.05133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.0141935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.05133333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.051875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281710&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281710&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.003666666666670.16319756261796412.2775526455449
Geometric MeanNaN
Harmonic Mean0.735113908832323
Quadratic Mean2.36348330506761
Winsorized Mean ( 1 / 20 )2.006333333333330.16186657801168512.3949820770814
Winsorized Mean ( 2 / 20 )2.004333333333330.16137410770174612.420414661798
Winsorized Mean ( 3 / 20 )2.009833333333330.1597907338528612.5779091495008
Winsorized Mean ( 4 / 20 )2.013833333333330.15870220338640112.6893848375258
Winsorized Mean ( 5 / 20 )2.024666666666670.15499798917351913.0625350526327
Winsorized Mean ( 6 / 20 )2.028666666666670.15315799358217213.2455813713585
Winsorized Mean ( 7 / 20 )2.029833333333330.15252479499580513.3082187285626
Winsorized Mean ( 8 / 20 )2.059166666666670.14548774225002414.1535405995094
Winsorized Mean ( 9 / 20 )2.053166666666670.14447498789776814.2112257390844
Winsorized Mean ( 10 / 20 )2.043166666666670.14226804725342714.3613882815662
Winsorized Mean ( 11 / 20 )2.05050.13923974873260414.726398306979
Winsorized Mean ( 12 / 20 )2.06850.13504504898083915.3171109611985
Winsorized Mean ( 13 / 20 )2.083666666666670.13199554149863515.785886727759
Winsorized Mean ( 14 / 20 )2.055666666666670.12680791262508616.2108706319009
Winsorized Mean ( 15 / 20 )2.065666666666670.12296969602044116.7981765712692
Winsorized Mean ( 16 / 20 )2.044333333333330.11970664865653917.0778595531391
Winsorized Mean ( 17 / 20 )2.02450.11420281913466517.7272331396019
Winsorized Mean ( 18 / 20 )1.99750.10942985912353518.2537016496114
Winsorized Mean ( 19 / 20 )2.01650.10285523395793919.6052249594281
Winsorized Mean ( 20 / 20 )2.019833333333330.10043000532643720.1118513014918
Trimmed Mean ( 1 / 20 )2.012931034482760.16052187436253712.5399173319929
Trimmed Mean ( 2 / 20 )2.020.15874610129173212.7247219526217
Trimmed Mean ( 3 / 20 )2.02870370370370.15674939746490612.9423381302496
Trimmed Mean ( 4 / 20 )2.035961538461540.15488726489839713.1447962477553
Trimmed Mean ( 5 / 20 )2.04260.15283385937490613.3648394953466
Trimmed Mean ( 6 / 20 )2.047083333333330.1513224676442613.5279536819725
Trimmed Mean ( 7 / 20 )2.051086956521740.14975801036244113.6960083240806
Trimmed Mean ( 8 / 20 )2.055227272727270.1477232029037713.9126909810241
Trimmed Mean ( 9 / 20 )2.054523809523810.14674565067087714.0005771900642
Trimmed Mean ( 10 / 20 )2.054750.1454264231537114.1291379890998
Trimmed Mean ( 11 / 20 )2.056578947368420.14392747319870514.2889950171578
Trimmed Mean ( 12 / 20 )2.05750.14235456237357314.4533477936634
Trimmed Mean ( 13 / 20 )2.055882352941180.14091888265200414.5891190325297
Trimmed Mean ( 14 / 20 )2.0518750.13928926554464914.731034670739
Trimmed Mean ( 15 / 20 )2.051333333333330.13794446103233714.8707191139227
Trimmed Mean ( 16 / 20 )2.049285714285710.13651455779438315.0114811738418
Trimmed Mean ( 17 / 20 )2.050.13473050023030315.2155599251529
Trimmed Mean ( 18 / 20 )2.053750.13306968385349715.4336430396955
Trimmed Mean ( 19 / 20 )2.062272727272730.13118166218156915.7207394156839
Trimmed Mean ( 20 / 20 )2.06950.12967667282007315.9589227190571
Median2.255
Midrange1.735
Midmean - Weighted Average at Xnp2.0141935483871
Midmean - Weighted Average at X(n+1)p2.05133333333333
Midmean - Empirical Distribution Function2.0141935483871
Midmean - Empirical Distribution Function - Averaging2.05133333333333
Midmean - Empirical Distribution Function - Interpolation2.05133333333333
Midmean - Closest Observation2.0141935483871
Midmean - True Basic - Statistics Graphics Toolkit2.05133333333333
Midmean - MS Excel (old versions)2.051875
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')